Eli Bar-Yahalom wrote in to tell me of a really fascinating related
matter. He says that the word for "perimeter" is normally written
"QW", but in the original, canonical text of the book of Kings, it is
written "QWH", which is a peculiar (mis-)spelling.
(M. Bar-Yahalom sent me the Hebrew text itself, in addition to
the Romanizations I have shown, but I don't have either a Hebrew
terminal or web browser handy, and in any event I don't know how to
type these characters. Q here is qoph, W is vav, and H is hay.)
M. Bar-Yahalom says that the canonical text also contains
a footnote, which explains the peculiar "QWH" by saying that it
represents "QW".

The reason this is worth mentioning is that the Hebrews, like the
Greeks, made their alphabet do double duty for both words and
numerals. The two systems were quite similar. The Greek one went
something like this:

Α

1

Κ

10

Τ

100

Β

2

Λ

20

Υ

200

Γ

3

Μ

30

Φ

300

Δ

4

Ν

40

Χ

400

Ε

5

Ξ

50

Ψ

500

Ζ

6

Ο

60

Ω

600

Η

7

Π

70

Θ

8

Ρ

80

Ι

9

Σ

90

This isn't quite right, because the Greek alphabet had more letters
then, enough to take them up to 900. I think there was a "digamma"
between Ε and Ζ, for example. (This is why we have F
after E. The F is a descendant of the digamma. The G was put in in
place of Ζ, which was later added back at the end, and the H is a descendent of Η.) But it should
give the idea. If you wanted to write the number 172, you would use
ΒΠΤ. Or perhaps ΤΒΠ. It didn't matter.

Anyway, the Hebrew system was similar, only using the Hebrew
alphabet. So here's the point: "QW" means "circumference", but it
also represents the number 106. (Qoph is 100; vav is 6.) And the odd
spelling, "QWH", also represents the number 111. (Hay is 5.) So the
footnote could be interpreted as saying that the 106 is represented by
111, or something of the sort.

Now it so happens that 111/106 is a highly accurate approximation of
π/3. π/3 is 1.04719755 and 111/106 is 1.04716981. And
the value cited for the perimeter, 30, is in fact accurate, if you put
111 in place of 106, by multiplying it by 111/106.

It's really hard to know for sure. But if true, I wonder where the
Hebrews got hold of such an accurate approximation? Archimedes pushed
it as far as he could, by calculating the perimeters of 96-sided
polygons that were respectively inscribed within and circumscribed
around a unit circle, and so calculated that 223/71 < π <
22/7. Neither of these fractions is as good an approximation as
333/106.